- On Mon, 05 March 2001, Chris Harrison wrote:
> Dear All,

My mail receiving operation M could be nilpotent.

>

> Please be aware that I have e-mailed Phil Carmody TWICE to ask him to

> correct his assertion copied below:

Or maybe M is idempotent.

Perhaps neither of the above. If so, and M^2 == I...

> >On Sun, 04 March 2001, "�� ����" wrote:

You should see my inbox! One tediously long meeting and lunch - that's all it takes.

> > who can give me a twin primes table below 1024 bits,or an address, thank you!

>

> >on't be fooled by the name, these only go up to 15 digits:

> >http://www.meganumbers.com/

>

> >If you want anything larger, your best bet is to generate them yourself.

>

> and he has not responded, hence this e-mail.

At least we know the primenumbers list is "active" now!

> There are IN FACT bulk sequences of primes up to 19 digits in length

My mistake, sorry. However, as has been noted elsewhere, 10^19 is still "small" compared to the ~1000 bit range being mentioned. I'd not actually perused the 'meganumbers' site before, so wasn't previously aware of what it contained. However, as this side of the globe was awake, and the Americans were probably asleep, I thought that I'd do the "run around the primepages finding pointers" job. It's only those that actually do things that get criticised, so I don't feel too bad at having one bogus character in my entire reply.

> at the MegaNumberS web site.

Phil

Mathematics should not have to involve martyrdom;

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http://www.shopping.altavista.com - A carefully constructed dump of a sieve will beat most run-length compression schemes, even with huffman (or other entropy) compresion.

For broad ranges, I'd use a 480/2310 comb to the sieve.

For small ranges (a million primes) a 8/30 comb is fine.

With the right code, I guestimate that generating primes should be faster than reading them off disk still, but it's not by a huge margin. Race Dan Bernstein's Primegen and Eratspeed against your hard disk for primes up to a billion if you don't believe me. (there are links on the primepages)

However, my current sieving job is generating 17 digit numbers, and I store the deltas, which average around 7-8 digits. This gives me roughly 2:1 compression. I then BZIP2 them, which gives an almost exact log(10)/log(256) ratio, as the numbers are essentially unpredictable. Even then, I think I could fill a CD in a month.

Twins fall into this latter catagory, and their density means that hard disk storage is worthwhile.

Phil

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